Volumetric Strain (εv)

When a member is subjected to stresses, it undergoes deformation in all directions. Hence, there will be change in volume. The ratio of the change in volume to original volume is called volumetric strain.

Thus,

Where,

           εv = Volumetric strain 

          δV = Change in volume

           V = Original volume

It can be shown that volumetric strain is sum of strains in three mutually perpendicular directions.

For example consider a bar of length L, breadth b and depth d as shown in Fig. 1.

Fig. 1 Rectangular Bar

Now,

Volume, V = L b d

Since volume is function of L, b and d, by using product rule (The derivative of the product of two differentiable functions is equal to the addition of the first function multiplied by the derivative of the second, and the second function multiplied by the derivative of the first function.) we may write as;

Consider a circular rod of length ‘L’ and diameter ‘d’ as shown in Fig. 2.

Fig. 2 Circular Rod

Volume of the bar

                                                                                         (Since V is function of d and L)

Dividing the equation by V

In general for any shape volumetric strain may be taken as sum of strains in three mutually perpendicular directions.